Abstract
We describe a powerful method for determining the equation of state of an ultracold gas from in situ images. The method provides a measurement of the local pressure of a harmonically trapped gas and we give several applications to Bose and Fermi gases. We obtain the grand-canonical equation of state of a spin-balanced Fermi gas with resonant interactions as a function of temperature (Nascimbène et al 2010 Nature463 1057). We compare our equation of state with an equation of state measured by the Tokyo group (Horikoshi et al 2010 Science327 442), which reveals a significant difference in the high-temperature regime. The normal phase, at low temperature, is well described by a Landau Fermi liquid model, and we observe a clear thermodynamic signature of the superfluid transition. In a second part, we apply the same procedure to Bose gases. From a single image of a quasi-ideal Bose gas, we determine the equation of state from the classical to the condensed regime. Finally, the method is applied to a Bose gas in a three-dimensional optical lattice in the Mott insulator regime. Our equation of state directly reveals the Mott insulator behavior and is suited to investigate finite-temperature effects.
Highlights
We describe in more detail the procedure used to determine the equation of state of a spin-unpolarized Fermi gas in the unitary limit [1]
From an in situ image of 7Li, we obtain the equation of state of a weakly interacting Bose gas
We have shown on various examples of Fermi and Bose gas systems how in situ absorption images can provide the grand-canonical equation of state of the homogeneous gas
Summary
If one independently determines temperature T and chemical potential μ0, each pixel row of the absorption image at a given position z provides an experimental data point for the grand-canonical equation of state P(μz, T ) of the homogeneous gas. The large number of data obtained from several images allows one to perform an efficient averaging, leading to a low-noise equation of state. This formula is valid in the case of a two-component Fermi gas with equal spin populations if n(z) is the total integrated density. The method can be generalized to multicomponent Bose and Fermi gases, as first demonstrated on spin-imbalanced Fermi gases in [1, 14]
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